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Maths / Ratio and Proportion / Ratio and Its Simplest Form
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## Ratio and Its Simplest Form

Ratio:

A ratio is the relationship, or comparison, of one quantity to another. In  other words we can say that ratio indicates how many times one quantity is contained in the  another. quantity For example, if there are ten boys and seven girls  in a group of students, then the ratio of boys and girls is ten to seven. And the ratio of girls to boys is seven to ten.

Converting Ratio in Simplest Form:

To simplify a ratio means to reduce it to its smallest, simplest, terms.

Here we will learn how to make the ratio in simplest form.

1. A ratio between two quantities of same kind and in the same units is obtained on dividing one quantity by the other. Ratio does have units as it is being used to compare to quanties in the same units. The ratio is independent of the units used in the quantities compared.

2. The ratio must always be expressed in its simplest form or in its lowest terms.

A ratio is said to be is the simplest form or in the lowest term if two quantities of a ratio (i.e., antecedent and consequent) have no common factor other than 1 or their HCF is 1. (i.e. antecedent and consequent are co-prime)

ILLUSTRATION 1: The ratio between 36 kg and 24 kg

$\fn_jvn \large =\frac{36 kg}{24 kg}=\frac{3 \; X\;12}{2\;X\;12}=\frac{3}{2}=3:2$

ILLUSTRATION 2: The ratio between 90 cm and 1.5m

Solution:  As the two quantities are in diffrent units we will first convert them so that they are in same units

As im= 100cm

1.5 m = 1.5 X 100 = 150 cm

$\fn_jvn \large =\frac{90\; cm}{1.5\; m}=\frac{ 90\; cm}{150\;cm}= \frac{3 \; X\;30}{5\;X\;30}=\frac{3}{5}=3:5$

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